Faculty of Education - Theses
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ItemRemediating the elementary mathematics of prospective primary school teachers( 1980)Three areas are reviewed: the knowledge of prospective primary teachers of basic mathematics, remediation programs in mathematics and the use of calculators as a learning aid in mathematics. A remediation program is described involving a diagnostic pre-test and consequent assignment to one of three treatments: self-study, group tutorials or individual tutorials. The purpose of the 10 week program is to help prospective primary teachers meet a competency requirement in mathematics which is mandatory for progress beyond the third semester of a six-semester course of primary teacher training at a Victorian university. The program covers understanding and knowledge of place value, whole number decimals and fraction operations, percentages, averages and measurement including metrics. The group tutorials were given one of two treatments: the use of calculators during the remedial program, or the same program without calculators. Seven hypotheses related to the effects of the program are described. Post-testing after the 10 weeks of the program showed very large gains by each of the three groups. However the calculator group showed no difference from the non-calculator group, a finding consistent with the literature. Discussion of the results and pointers for future study conclude the study, with one recommendation being that mathematics specialists be appointed to primary schools.
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ItemTeacher beliefs about mathematical problem solving in Free Wesleyan Church secondary schools in Tonga( 2001)It is clear from the literature that attention should be paid to teachers' beliefs about how the mathematics classroom operates and about the nature of mathematical problem solving. The introduction of a mathematical problem-solving curriculum which ignores these aspects is likely to be frustrated. This research seeks to learn more about the use of mathematical problem solving by Tongan teachers and what these teachers consider to be good teaching of mathematics and mathematical problem solving. Five mathematics teachers in the Free Wesleyan Church of Tonga education system were interviewed about their beliefs using the Kelly Repertory Grid technique through Enquire Within software. Surveys were also conducted of the material produced for schools by the Tongan Government's Ministry of Education. It was found that the Ministry of Education has implemented a minimal problem-solving curriculum throughout the Kingdom and that the beliefs of the majority of teachers interviewed were compatible with this minimalist model. Recommendations for the Free Wesleyan Church's Education Department are made on possible approaches to fulfilling the Ministry of Education's stated aim of preparing students to apply the principles of mathematics to unfamiliar situations.
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ItemEvaluating the foundations for teaching arithmetic CD-ROM: linking theory and practice( 2005)Lack of mathematical content knowledge (MCK), pedagogical content knowledge (PCK) and the ability to translate this knowledge into practice are recognised as major issues for pre-service teacher education today. Multimedia has been suggested as a way of facilitating the transfer of MCK and PCK to the classroom. In this context the Foundations for Teaching Arithmetic (FTA) CD-ROM was developed in 2001. The aim of this study is to evaluate how pre-service teachers in the Faculty of Education, University of Melbourne have used FTA, if at all, to improve their MCK and PCK and to support the translation of these into practice. Also under investigation is what conditions facilitate or obstruct student use of FTA as a self-help resource in improving pre-service teachers' conceptual understanding of, and confidence in, their ability to do and to teach mathematics. Questionnaires designed to find out why students did or did not use FTA and their rating of particular features of the resource were completed by 389 students in various education courses. Forty-four student users and non-users of FTA were interviewed individually or in focus groups about their experience of FTA and the factors that contributed to their decisions to use or not use it. The impact of these factors was determined through the development of a framework which mapped the action profile of each student. A four phase needs-based progression model was proposed to explain the factors which contributed to students being able to make the successful translation of PCK on FTA into practice. The design and content of FTA facilitated students' use of FTA for the purposes under investigation. Factors hindering student use of FTA did evolve from the content of FTA, but were attributed to circumstantial factors.
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ItemThe march of the calculator into Malaysian classrooms?( 1995)Calculators are used extensively in the workplace and are part of the technological change that is taking place in Malaysian society. However they are not used widely in the classrooms. About 200 primary, secondary and college teachers in Malaysia were surveyed about their attitudes toward the student use of calculators in the classroom and their current teaching practices. As many as 98% of the primary teachers and 83% of the lower secondary teachers have never used calculators in their mathematics lessons. The upper secondary teachers were using calculators in their classrooms because the present Malaysian national mathematics curriculum encourages and allows the use of calculators only at these levels. Most Malaysian teachers held more conservative views on calculator use than the teachers surveyed in Victoria, Australia in 1980. They felt that calculators should only be used after students have mastered basic number facts, acquired paper and pencil skills and understood the meaning of the four operations. About 29% of the teachers surveyed supported the introduction of calculators into primary classes. Although teachers believed that calculator use would enhance mathematics learning, many would not allow calculators to be used in class if they were not allowed on tests or examinations. Teachers also believed that parents would be against calculator use in the classrooms if they were not allowed on tests and examinations. It is recommended that the Malaysian Ministry of Education must allow calculator use on tests and examinations in order to encourage their use in primary and lower secondary classrooms.
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ItemTrainee-teachers: can attitudes and achievement in mathematics be improved?( 1988)The aim of the investigation was to compare the effects of different class-groupings upon the Attitude to, and Achievement in, Mathematics of Primary Teacher Trainees. The experiment was of the pre-test, post-test design, with students randomly assigned to Experimental or Control classes. Lecturers taking part were assigned one Experimental and one Control group each. The treatment comprised the First Year Mathematics Education Course at Phillip Institute of Technology, with students assigned to classes which were either homogeneous (Experimental) or heterogeneous (Control) with respect to school Mathematics background. The sample was drawn from an entire entry cohort (with depletions), to give a sub-population of about one-third. The experimental conditions extended over ten months (the time between dependent variable measurings) and subjects were not treated as special in other than those (grouping) ways mentioned above. Simple graphical analyses showed results of the treatment to be quite varied. Predicted outcomes were supported in few instances (measured by Effect Sizes) but in the main, hypotheses remain unsupported by this investigation - which matches the results of the majority of studies in this field.
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ItemAn investigation of the effect of teachers' reflection on their development of pedagogical content knowledge for teaching primary mathematics( 2008)In recent years, teachers' pedagogical content knowledge (PCK) has become the subject of an increasing volume of research. Another body of literature has grown around the subject of reflection, and its effect on practice. Although a link between the two has often been assumed, few have attempted to map this link explicitly. This study investigates the possibility of such a link, and explores possible descriptions of the link. This case study compared two primary (elementary) teachers, investigating both their PCK and their reflection. The teachers were asked to complete a written questionnaire about mathematics teaching, including some questions requiring a response to hypothetical classroom situations. They were then interviewed about the questionnaire. The teachers were observed as they taught, and interviewed about those lessons. The questionnaire and first interview were used to investigate the teachers' PCK, and all interviews were used to investigate the teachers' reflection. One teacher was found to have both rich and well-connected PCK, and a strong tendency to reflect. The second teacher was found to have much weaker PCK than the first, and also demonstrated less reflection. Some examples of the first teacher's reflection were examined, to investigate the possibility that the teacher's reflection had an influence on the development of PCK. PCK was observed to develop during reflection, suggesting that reflection influences the development of PCK.